Please help me answer these question with shown work and explanation so that I can learn from it!!

Graded Problems Your work on the graded problems should demonstrate your best work. Write up thorough solutions that a reader could follow from start to finish. The original problem, your assumptions and reasoning, your mathematical work, and your answer should all be shown and/or explained clearly. See \"Graded Problem Guidelines\" in the syllabus for more information on expectations and the grading rubric. 1. For the quadratic function P(x)=2x"+10x+12, find the following algebraically (without using the graph): d. b C. d. e The vertex The vertical intercept The horizontal intercepts Write the function in vertex form Write the function in factored form Explain in detail how the information provided in the graph enables you to find formulas for the functions fand g, and then determine the formulas. A water balloon is tossed vertically from a window on the fourth floor of a dormitory from an initial height of 56.3 feet. A person two floors above observed the balloon reach its highest point 1.2 seconds after being thrown, and it hits the ground after exactly 3.2 seconds. a. b. What is the exact maximum height the balloon reaches? Find the maximum possible area of a garden plot that uses 60 feet of boundary wall material Sketch a graph of the height of the balloon as a function of time, and use it to write a function. and separates three sections, as shown below: N